Question

How do you describe the transformation of `f(x)=sqrt(x-9)` from a common function that occurs and sketch the graph?

Answer 1

Shift `sqrt(x)` to the right by 9 units.

Explanation:

First evaluate the basic function `f(x)=sqrt(x)`
graph{y=sqrt(x) [-1,5,-1, 3]}
Subtracting a number on the inside of a function (i.e., next to the
`x` value), shifts the function to the right that many units. So putting `x-9` inside the square root function, shifts the graph of the square root function to the right by 9 units.
graph{y=sqrt(x-9)[-1,20,-1,5]}
Just remember that when you add or subtract a number on the inside of a standard function, it does the opposite of what you might expect. Subtracting 9 moves the graph to the right by 9 units. Adding 9 would have moved the graph to the left by 9 units.